If tenant fails to immediately notify landlord of the need for repair or maintenance, and additional damage occurs to the premises which could have been prevented if landlord had been able to make prompt repairs, tenant shall be responsible for the cost of repairing the additional damage even if the original damage was not tenants fault.Would this be a situation where the tenant should pay for all/some of the dry wall needing replacement ?

If they prevented you from inspecting entire rooms then yes you are in the right, if they prevented you from tearing open the drywall to check for some unknown boogeyman then you are not in the right. 

I believe it tends to give me a slightly lower return, because the sponsor is going to be more careful, and if there is a severe downturn will prevent me from taking catastrophic losses.

I want to prevent that. 

If the unit has been inspected, but not deleaded, you also cannot do any construction or remodeling in the unit, they consider that unauthorized deleading and it will prevent you from ever getting a lead cert.

That way you don't carry the liability of making a mistake in how you screen for what is legitimate or not, especially since you've made it clear (and your attorney gave you dangerously bad advice) that you are trying to prevent "pitbulls" from residing in your units for insurance reasons.

When rats get poisoned, they separate themselves from the pack to prevent infecting the others.

The construction rehab will be financed by hard money lenders.I would like some advice on this renegotiation strategy if it will work or find out an alternative method to save this deal and prevent the property being foreclosed on.

Lots of people come up with repeated concerns that prevent them from pulling the trigger. 

Unless there is some weird circumstances preventing, but most likely get a higher price with inspection.